Use of pronoun ТЫ as particle

Question

I often see phrases such as—

"да ты не бойся, ты вспомни и т.п."

But I have yet to come across, in a grammar, an explanation of the use of these pronouns in such cases. What meaning do they add, and where can I read about this structure?

Answer 1

"Ты" (or "вы", both plural and polite singular) here is not a particle, it's the subject of the sentence, which is usually omitted in neutral sentences. It adds a shade of familiarity and supportive, patronizing attitude towards the person you are talking to. This construction is acceptable (and widely used) wherever such attitude itself is appropriate. Once you've used it, the conversation gets less formal and more personal. Such sentences sound like either kindly advices or to-do instructions, pronounced in a patronizing tone. For example, mother can tell her little son (in mentor tone, she may be slightly irritated, because she has to repeat it every day, but not angry):

Вань, ты руки-то помой после улицы!

Vanya, wash your hands after playing outside!

Or someone shows his pet snake to guests, who look pretty frightened, and says with a calming smile:

Вы не волнуйтесь, она не ядовитая.

Don't worry, it is not venomous.

Or a husband says to his wife, who is going to file for divorce, in a calm and supportive, without any anger:

Маш, ты все-таки подумай еще раз, может еще не поздно все исправить?

Masha, try to think once more, please, maybe it's still not too late to get it right?

And about English translation, I wonder myself, how to express this properly in English. Any suggestions are welcome!